A computer search shows that the set of initial 70 Mersenne numbers $2^p-1$ (all with prime exponents) has 54 members, or approx 77%, that lie between twin practical numbers. (Edit: Alternatively, $2^p-2$ is a practical number 77% of the time for the first 70 prime $p$.) Is it known whether this percentage will increase, decrease, or converge to a limit as the sample size tends to infinity?
A similar search shows that for the first 13 Mersenne primes $2^p-1$, then $2^p-2$ is a practical number with one exception, namely $p=107$. Are there any other exceptions? My computing power is unable to cope with larger Mersenne primes.